The problem of cognitive access of multiple primary channels by multiple cognitive users is considered. The primary transmission on each channel is modeled by a continuous time Markov on-off process. Cognitive access of the primary channels is realized via channel sensing. Each cognitive user adopts a slotted transmission structure, senses one channel in each slot and makes the transmission decision based on the sensing outcome. The cognitive transmissions in each channel are subject to collision constraints that limit their interference to the primary users. The maximum throughput region of this multiuser cognitive network is characterized by establishing inner and outer bounds.